Bulletin of the
Korean Mathematical Society BKMS

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

Keywords: analogue of Wiener measure, conditional analytic Feynman integral, conditional analytic Wiener integral, operator-valued Feynman integral, simple formula for conditional expectation, Wiener space

MSC numbers: Primary 60H05; Secondary 28C20, 46T12